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arXiv · 2412.17400

The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces

Martina Rovelli
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Abstract

This note is a contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics". The content is a streamlined exposition based on a talk about a result by Bergner-Osorno-Ozornova-Rovelli-Scheimbauer from WITII. We discuss how a generalized version of Waldhausen's S-construction describes a correspondence between 2-Segal spaces and certain double Segal spaces, which satisfy further conditions of stability and augmentation.

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Martina Rovelli. 2024-12-23. The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces. https://arxiv.org/abs/2412.17400

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